Overview

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• This site provides a set of computer programs which support the Bayesian model building of in silico biological pathways based on time course data of biochemical reactions. It is organized by follows: (1) Pathway modeling with kinetic rate equations (difference equations) which are described based on the architecture of hybrid functional Petri net, (2) Parameter estimation of rate equations (3) Test for the ability of the constructed models in terms of predictability and biological robustness. The programs have been developed by FORTRAN 77. Once user has specified hypothetical in silico pathways in the model indication file and time course measurements of biological components have be given, the program explores the model parameters for which solution fits data by solving the optimization problem of smoothness prior. For the technical details, see Yoshida et al. (2008) (submitted for publication).

References

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• R.Yoshida, M.Nagasaki, R.Yamaguchi, S.Imoto, S.Miyano, T.Higuchi (2008) Bayesian learning of biological pathways on genomic data assimilation, Bioinformatics, 24(22):2592-2601 [PubMed] [Bioinformatics]

Download

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• ASIM-V4.1 (Last modified; 11-July-2008): Set of FORTRAN programs (FORTRAN 77) and text-formatting files for which user indicates the input parameters.

Author

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• Ryo Yoshida, Department of Statistical Modeling, Institute of Statistical Mathematics, Research Organization of Information and Systems, Japan

Usage

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• Body of the program consists of "opt-pet-01.for" and "ran-cls-gauss.for". The source code "opt-pet-01.for" includes main program and a set of subroutines and functions, which are required for the parameter estimation algorithm and the model evaluator. The supplementary codes in "ran-cls-gauss.for" are comprised of the subroutines for the generation of random numbers. After specifying the input files by following the formatting rules shown in below, and compilations of the programs, run the "opt-pet-01.for". For the details on the required input files and output files, see below.

Body of Program

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• Make sure the following files are all right installed:
  
  
  • opt-pet-01.for
    • Fortran source codes which are comprise of main program and a set of subroutines involved in the algorithms of parameter learning and model evaluators
    
    
  • ran-cls-gauss.for
    • Fortran source codes which are comprise of subroutines and functions for generating random numbers

Input Data Files

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• Make sure the following files are all right installed:
  
  
  • prm_opt-pet.dat
    • Text file which contains the parameters indicating experimental environments
    
    

    Row	Value	Name of variable	Description
    1	Character	file	This parameter indicates the file name for input- and out-files. For example, if we set a string "circadian12.dat" to file, the program loads the input data files having the names "data_circadian12.dat"and "petri-net_circadian12.dat" as files for time course data and model indicator. Besides, all output files are also named with this string, e.g. "simulation_file". The length of string is limited by 20. In what follows, "***" indicates the file name specified here.
    2	Integer	l	Number of entire time steps for simulation
    3	Integer	n	Number of observed time points in which the time course measurements are included
    4	Integer	k	Number of biological entities which span the in silico biological pathway
    5	Integer	ix	Seed for random number generator
    6	Integer	id_noise	Variable which indicates whether or not the noise components are included during the run of initial simulation. Before running the algorithm of parameter learning, an initial sequence of state variables are generated. The current program draws it by running simulation with the prior means of rate constant parameters and initial state variables that are respectively indicated in "prior-kinetic_***.dat" and "ini-state_***.dat". The variable indicates whether or not stochastic simulation is performed during this step. 0; Non-stochastic initial simulation 1; Stochastic initial simulation. If this option is chosen, a variance parameter must be set at the 7th row of "prm_opt-pet.dat" (dsp_noise).
    7	Positive real number	dsp_noise	Variance parameters of initial stochastic simulation. If id_noise is sets to 1 in the 6th row of "prm_opt-pet.dat", the program executes a stochastic simulation by adding the Gaussian noises with the specified values of variance during the generation of initial sequence of state variables.

  
  
  
  • src-option_***.dat
    • Text file which indicates the smoothing parameter for system model
    
    

    Row	Value	Name of variable	Description
    1	---	---	Invalid for the current version
    2	Positive real number	smth	Value of smoothing parameter (variance)

  
  
  
  • data_***.dat
    • Text file which specifies time course measurements
    
    

    Row	Value	Name of Variables	Description
    1	Character	--- (Invalid)	Names of biological entities
    2	Integer	iobs_node	Indicator variable for observability of biological entities 0; Unobservable entity (the corresponding values of observations are ignored, but blank is not allowed) 1; Time course measurements of corresponding biological entity are observable. 2; Indication of input entity. If it is chosen, you must specify a series of input values in "input-series-***.dat" in the following way: Row Value Description 1 Integer Total number of input entities 2 Character Names of entities 3 Integer Entity IDs which must be consistent to the order of entities in "data_***.dat" 4-last Positive numeric number Sequences of input variables with the time points (in the first column). The time points must cover the entities time points of simulation, thereby being successive positive integers ranging from one to total number of simulation time steps.
    3	Integer	---	Series of integers starting from 1 to the number of biological entities.
    4 to last row	Positive real number (1st column; positive integer)	y (1st column; iobs_time)	Time course measurements for which the learning algorithm uses to train, and the corresponding observable time points indicated in the first column. If an entity is called "unobservable" or "input variable" in the second row (iobs_node=0 or 2), the corresponding values have no effect during execution of the program. However, the program does not allow the blanket spaces during the read operations, and thereby, arbitrary numeric values must be placed.

  
  
  
  • petri-net_***.dat
    • Text file which is used for building model of biological pathway
  
  
  • This file is used to specify a set of child-parent regulatory relationships with biochemical rate equations. Currently, the program allows to use at most two parent entities per one child. For the list of regulatory equations that user can use, see the plain text comments in "petri-net_***.dat" (on the 1-20 lines) (see also Yoshida et al. 2008).
  
  

  Row	Value	Name of variable	Description
  1	Integer	t	Number of regulatory equations that user has specified in this file
  2	Positive real number	stp	Scale factor of time interval for simulation

  
  In below of the 25th line, parent-child regulatory relationships are specified with rate equations according to the following format:
  
  

  Column	Value	Name of variable	Description
  1	Integer	irg(,1)	ID for child entity
  2-3	Integer	irg(,2:3)	IDs for parent entities. If the number of parent entities is one, the corresponding ID must be indicated in the second column.
  4	Integer	irg(,4)	ID for regulatory equation. For the current version, user can choose this from 1-14 in which the reference table for these regulation IDs are available on the 7-20 lines of "petri-net_***.dat".
  5	Positive real number	prm(,1)	Rate constant without sign (where the sign is specified in the 8th column)
  6-7	Positive real number	prm(,2:3)	Threshold parameters. If user specifies an indicator function (irg(,4)=5-9) in the 4th column, these parameters become valid. Particularly, for the specified indicator functions defined over single parent (irg(,4)=5-6), the threshold value must be specified in the 6th column. On the other hand, for the indicator functions over two parents (irg(,4)=7-9), the corresponding threshold values are specified in the 6th and the 7th column, respectively.
  8	+1 or -1	prm(,4)	Sign for the rate constant. Rate constant is computed as the value in the 5th column times the sign specified in the 8th column (prm(,1) times prm(,4)).
  9	Integer	id_clst	Estimation parameter ID. If it is set to non-zero integer value, the program seeks estimates for the rate constant and the threshold parameters. For non-estimated regulation functions, put it as zero. These IDs must be consistent to the estimation parameter IDs specified in "prior-kinetic_***.dat" for which user specifies values of prior distributions of the estimated rate constants. (NOTICE) In order to model and estimate the regulatory functions following low of conserved mass, place the same IDs to the set of corresponding regulatory functions. For instance, suppose that reactants 1 and 2 bind, and generate its complex 3 with the rate constant k. Then, user can represent these reactions as follows: Child Parent 1 Parent 2 Rate constant Sign Estimation ID 1 1 2 k -1 1 2 1 2 k -1 1 3 1 2 k 1 1
  10-	---	---	Invalid (comments and descriptions can be written here)

  
  
  
  • prior-kinetic_***.dat
    • Text file which specifies the prior distributions of rate constant parameters
  
  

  Row	Value	Name of variable	Description
  1	Integer	nprm	Number of rate constant parameters to be estimated
  2	---	---	Invalid

  
  In below of the third line, values of prior distributions are specified with the estimation parameter IDs in the following ways.
  
  

  Column	Value	Name of variable	Description
  1	Positive real number	prior_prm(,1)	Prior mean
  2	Positive real number	prior_prm(,2)	Prior variance
  3	Integer	id_prm	Estimation parameter ID
  4	Positive real number ranging from 0 to 1	pr_prm	This value defines a frequency of updates for the rate constant parameter during the run of recursive estimation in the learning algorithm. At each step of iteration, the program determines whether or not update the corresponding rate constant with the probability specified here.
  5-	---	---	Invalid

  
  
  
  • ini-state_***.dat
    • Text file which specifies values of initial states and prior distributions
  
  

  Column	Value	Name of variable	Description
  1	Positive real number	x(1,)	Value of initial state variable that is only used for the run of initial simulation
  2	Positive real number	prior_node(,1)	Prior mean
  3	Positive real number	prior_node(,2)	Prior variance
  4-	---	---	Invalid

  
  
  
  Output Data Files

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  • est-model_opt-pet_***.dat
    • Tab-delimited text file which contains the estimated regulatory functions for the hypothetical model. The formatting rule of this file is the same to the model creation file "petri-net_***.dat".
    
    

    Row	Value	Description
    1	Integer	Number of regulatory equations that user has specified
    2	Positive real number	Time scale for the run of simulations

    
    In below of the 25th line, parent-child regulatory relationships are specified with rate equations according to the following format:
    
    

    Column	Value	Description
    1	Integer	ID for child entity
    2-3	Integer	IDs for parent entities. If the number of parent entities is one, the corresponding ID has to be indicated in the second column.
    4	Integer	ID for regulatory equation. For the current version, user can choose it from 1-14 in which the reference table for these regulation IDs are available on the 7-20 lines of "petri-net_***.dat".
    5	Positive real number	Rate constant (linear) without sign (where the sign is specified in the 8th column)
    6-7	Positive real number	Threshold parameters. If user sets an indicator function (Reg.ID; 5-9) in the 4th column, these parameters turn to be valid. Particularly, for the indicator functions defined over single parent (Reg.ID; 5-6) which is indicated in the third column, the threshold value corresponds to a value in the 6th column. On the other hand, for the indicator functions over two parents (Reg.ID; 7-9), the corresponding threshold values are specified in the 6th and the 7th column, respectively.
    8	+1 or -1	Sign for the rate constant. Rate constant is computed as the value in the 5th column times the sign specified in the 8th column.
    9	Integer	Estimation parameter ID. If it is set to non-zero integer value, the program seeks out estimates for the rate constant and the threshold parameters. For non-estimated regulation functions, put zero. These IDs have to correspond to the estimation parameter IDs specified in "prior-kinetic_***.dat" for which user specifies prior values for estimation of the rate constant. (NOTICE) In order to estimate the regulatory functions following low of conserved mass, place the same IDs to the set of corresponding regulatory functions. For instance, Suppose that reactants 1 and 2 bind and generate its complex 3 with the rate constant k. Then, user can represent these reactions as follows: Child Parent 1 Parent 2 Rate constant Sign Estimation ID 1 1 2 k -1 1 2 1 2 k -1 1 3 1 2 k 1 1

  
  
  
  • est-state_opt-pet_***.dat
    • Tab-delimited text file which contains the sequence of the estimated state variables. The estimates are computed as a local minima of the objective functions that Yoshida et al. (2008) defines.
  
  

  Column	Value	Description
  1	Integer	Time points (for simulation)
  2-last	Positive numeric number	The estimated state variables for each entity are shown in each column. Note that the estimate initial states are given in the first row which corresponds to the time point 1.

  
  
  
  • est-prm_opt-pet_***.dat
    • Tab-delimited text file which contains the estimated values of the rate constants. The estimates are computed as a local minima of the objective functions that Yoshida et al. (2008) defines.
    
    

    Column	Value	Description
    1	Integer	Estimation parameter IDs specified in "prior-kinetic_***.dat"
    2	Positive numeric number	Estimated values
    3	Positive numeric number	Prior means specified in "prior-kinetic_***.dat"
    4	Positive numeric number	Prior variances specified in "prior-kinetic_***.dat"

  
  
  
  • simulation_***.dat
    • Tab-delimited text file which contains result of the simulation with the estimated rate constants and the estimated initial state variables.
    
    

    Column	Value	Description
    1	Integer	Time points (for simulation)
    2-last	Positive numeric number	For each entity, series of the simulation path are shown in each column.

  
  
  
  • obj-fnc_***.dat
    • Tab-delimited text file which contains series of objective functions computed during the run of optimization algorithm. Note that the computed values shown are non-decreasing sequence.
    
    

    Column	Value	Description
    1	Integer	Number of iterations
    2-last	Positive numeric number	Values of the computed objective functions.

  
  
  
  • model_evaluator_bic.dat
    • Tab-delimited text file which contains score of BIC computed from Bayesian perturbed experiments
    
    

    Column	Value	Description
    1	Numeric number	Score of BIC